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ATLAS ATLAS (Automatically Tuned Linear Algebra Software) is a system for generating high-performance mathematical libraries. It generates a library that is specifically tuned to your processor and compiler. ATLAS's purpose is to provide portably optimal linear algebra software. In particular, ATLAS provides ANSI C and Fortran 77 interfaces to the BLAS, and a subset of LAPACK.

Apophenia 'Apophenia' is a statistical library for C. It provides functions on the same level as those of the typical stats package (OLS, probit, singular value decomposition, &c.) but doesn't tie the user to an ad hoc language or environment. It uses the GNU Scientific Library for number crunching and SQLite for data management, so the library itself focuses on model estimation and quickly processing data.

Autoclass AutoClass solves the problem of automatic discovery of classes in data (sometimes called clustering or unsupervised learning), as distinct from the generation of class descriptions from labeled examples (called supervised learning). It aims to discover the 'natural' classes in the data. AutoClass is applicable to observations of things that can be described by a set of attributes, without referring to other things. The data values corresponding to each attribute are limited to be either numbers or the elements of a fixed set of symbols. With numeric data, a measurement error must be provided.

Axiom Axiom is a general purpose Computer Algebra system. It was originally created under the name Scratchpad and has seen development at companies such as IBM and NAG. Axiom provides a mature, powerful, strongly typed environment designed to enable research into mathematical algorithms and theory. It is also useful for engineering or scientific purposes.

BLAS The BLAS (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations. The Level 1 BLAS perform scalar, vector and vector-vector operations, the Level 2 BLAS perform matrix-vector operations, and the Level 3 BLAS perform matrix-matrix operations. Because the BLAS are efficient, portable, and widely available, they are commonly used in the development of high quality linear algebra software, LAPACK for example.

Bc 'Bc' is an arbitrary precision numeric processing language. Its syntax is similar to C, but differs in many substantial areas. It supports interactive execution of statements. 'Bc' is a utility included in the POSIX P1003.2/D11 draft standard. This version does not use the historical method of having bc be a compiler for the dc calculator (the POSIX document doesn't specify how bc must be implemented). This version has a single executable that both compiles the language and runs the resulting 'byte code.' The byte code is not the dc language.

BigMath Based partly on Knuth's Seminumerical Algorithms and written in C, BigMath aims to be light-weight and fast. Its original implementation was for use within a kernel extension - thus size and speed were essential. BigMath supports only integer math, including add, sub, mul, div, mod, modpow, modinv, pow, gcd, factorial, radix conversion, scientific notation and various comparisons.

Bitwise enums A very simple, 0-overhead, and yet type-safe 1-file library for doing bitwise operations between masks represented by enums. Please note: This library has been subsumed into MiLi and is no longer being maintained individually.

C-Graph GNU C-Graph is a tool for visualizing the mathematical operation of convolution underlying natural phenomena susceptible to analysis in terms of engineering signals and systems theory. "C-Graph" is an abbreviation for "Convolution Graph". The package is derived from the BSc. Honours dissertation in Electrical Engineering "Interactive Computer Package Demonstrating: Sampling Convolution and the FFT", Adrienne Gaye Thompson, University of Aberdeen (1983). The package computes the linear convolution of two signals in the time domain then compares their circular convolution by demonstrating the convolution theorem. Each signal is modelled by a register of discrete values simulating samples of a signal, and the discrete Fourier transform (DFT) computed by means of the Fast Fourier Transform (FFT). GNU C-Graph is interactive, prompting the user to enter character or numerical values from the keyboard, dispensing with the learning curve for writing code. The software will be useful to students of signals and systems theory. C-Graph is written in contemporary Fortran. You can find pre-GNU development versions at: <http://codeartnow.com/code/download/c-graph-1/c-graph-version-2-preview>. Adrienne Gaye Thompson is the sole author of GNU C-Graph and looks forward to sharing further development with the FLOSS community.

Calc Calc is an arbitrary precision arithmetic system that uses a C-like language. It's useful as a calculator, an algorithm prototype, and as a mathematical research tool. More importantly, calc provides a machine-independent means of computation. Its features include:

• Arbitrary precision integers and floating-point, fractions and complex values
• Logarithm, numeric, trig, hyperbolic functions
• C-like syntax
• calc shell scripts, resource files, linkable program library
• User defined finctions and function loading
• Over 283 built-in functions plus hooks for built-in custom extensions
• Arrays, lists, dynamic strings, matrices, associate arrays, objects
• Numeric, relational, boolean and variable access operators
• Extensive string and binary block memory builtin functions
• Matrix inversion, determinant, and other matrix operations
• Fast and cryptographic pseudo-random numbers, cryptographic hashes
• Factoring, primality tests, pi(x), multiplicative inverse, modular exp
• Bernoulli numbers, Euler numbers, Catalan numbers
• Uses REDC, splint-point and other high speed multi-precision algorithms
• Extensive regression test suite
• Resource functions: large prime tests, factoring, quaternions, etc.
• File I/O, multi-precision printf and scanf, stdio-like functions
• GNU readline, user & system startup scripts, emacs-style line editing
• Online help

Choose Choose is a program that computes permutations and choose functions. It does so quickly and effectively. Choose falls into the category of programs that are simple but are useful and for some reason do not exist.

Coq A proof done with Coq is mechanically checked by the machine. In particular, Coq allows:

• to define functions or predicates,
• to state mathematical theorems and software specifications,
• to develop interactively formal proofs of these theorems,
• to check these proofs by a relatively small certification "kernel".

CrocoPat 'CrocoPat' is a tool for querying and manipulating relations. It is easy to use because of its simple query and manipulation language based on predicate calculus and its simple file format for relations. It is efficient because it internally represents relations as binary decision diagrams, a data structure that is well-known as a compact representation of large relations. CrocoPat is general, because it manipulates not only graphs (i.e. binary relations), but n-ary relations.

DUNE-Common DUNE, the Distributed and Unified Numerics Environment is a modular toolbox for solving partial differential equations (PDEs) with grid-based methods. It supports the easy implementation of methods like Finite Elements (FE), Finite Volumes (FV), and also Finite Differences (FD). DUNE is free software licensed under the GPL (version 2) with a so called "runtime exception" (see license). This licence is similar to the one under which the libstdc++ libraries are distributed. Thus it is possible to use DUNE even in proprietary software. The underlying idea of DUNE is to create slim interfaces allowing an efficient use of legacy and/or new libraries. Modern C++ programming techniques enable very different implementations of the same concept (i.e. grids, solvers, ...) using a common interface at a very low overhead. Thus DUNE ensures efficiency in scientific computations and supports high-performance computing applications. DUNE is based on the following main principles:

• Separation of data structures and algorithms by abstract interfaces.- This provides more functionality with less code and also ensures maintainability and extendability of the framework.
• Efficient implementation of these interfaces using generic programming techniques.
• Static polymorphism allows the compiler to do more optimizations, in particular function inlining, which in turn allows the interface to have very small functions (implemented by one or few machine instructions) without a severe performance penalty. In essence the algorithms are parametrized with a particular data structure and the interface is removed at compile time. Thus the resulting code is as efficient as if it would have been written for the special case.
• Reuse of existing finite element packages with a large body of functionality.- In particular the finite element codes UG, ALBERTA, and ALUGrid have been adapted to the DUNE framework. Thus, parallel and adaptive meshes with multiple element types and refinement rules are available. All these packages can be linked together in one executable.
• The framework consists of a number of modules which are downloadable as separate packages. The current core modules are:
• dune-common- contains the basic classes used by all DUNE-modules. It provides some infrastructural classes for debugging and exception handling as well as a library to handle dense matrices and vectors.
• dune-grid- is the most mature module. It defines nonconforming, hierarchically nested, multi-element-type, parallel grids in arbitrary space dimensions. Graphical output with several packages is available, e.g. file output to IBM data explorer and VTK (parallel XML format for unstructured grids). The graphics package Grape has been integrated in interactive mode.
• dune-istl (Iterative Solver Template Library)- provides generic sparse matrix/vector classes and a variety of solvers based on these classes. A special feature is the use of templates to exploit the recursive block structure of finite element matrices at compile time. Available solvers include Krylov methods, (block-) incomplete decompositions and aggregation-based algebraic multigrid.

DUNE-Grid DUNE, the Distributed and Unified Numerics Environment is a modular toolbox for solving partial differential equations (PDEs) with grid-based methods. It supports the easy implementation of methods like Finite Elements (FE), Finite Volumes (FV), and also Finite Differences (FD). DUNE is free software licensed under the GPL (version 2) with a so called "runtime exception" (see license). This licence is similar to the one under which the libstdc++ libraries are distributed. Thus it is possible to use DUNE even in proprietary software. The underlying idea of DUNE is to create slim interfaces allowing an efficient use of legacy and/or new libraries. Modern C++ programming techniques enable very different implementations of the same concept (i.e. grids, solvers, ...) using a common interface at a very low overhead. Thus DUNE ensures efficiency in scientific computations and supports high-performance computing applications. DUNE is based on the following main principles:

• Separation of data structures and algorithms by abstract interfaces.- This provides more functionality with less code and also ensures maintainability and extendability of the framework.
• Efficient implementation of these interfaces using generic programming techniques.
• Static polymorphism allows the compiler to do more optimizations, in particular function inlining, which in turn allows the interface to have very small functions (implemented by one or few machine instructions) without a severe performance penalty. In essence the algorithms are parametrized with a particular data structure and the interface is removed at compile time. Thus the resulting code is as efficient as if it would have been written for the special case.
• Reuse of existing finite element packages with a large body of functionality.- In particular the finite element codes UG, ALBERTA, and ALUGrid have been adapted to the DUNE framework. Thus, parallel and adaptive meshes with multiple element types and refinement rules are available. All these packages can be linked together in one executable.
• The framework consists of a number of modules which are downloadable as separate packages. The current core modules are:
• dune-common- contains the basic classes used by all DUNE-modules. It provides some infrastructural classes for debugging and exception handling as well as a library to handle dense matrices and vectors.
• dune-grid- is the most mature module. It defines nonconforming, hierarchically nested, multi-element-type, parallel grids in arbitrary space dimensions. Graphical output with several packages is available, e.g. file output to IBM data explorer and VTK (parallel XML format for unstructured grids). The graphics package Grape has been integrated in interactive mode.
• dune-istl (Iterative Solver Template Library)- provides generic sparse matrix/vector classes and a variety of solvers based on these classes. A special feature is the use of templates to exploit the recursive block structure of finite element matrices at compile time. Available solvers include Krylov methods, (block-) incomplete decompositions and aggregation-based algebraic multigrid.

DUNE-Grid How To DUNE, the Distributed and Unified Numerics Environment is a modular toolbox for solving partial differential equations (PDEs) with grid-based methods. It supports the easy implementation of methods like Finite Elements (FE), Finite Volumes (FV), and also Finite Differences (FD). DUNE is free software licensed under the GPL (version 2) with a so called "runtime exception" (see license). This licence is similar to the one under which the libstdc++ libraries are distributed. Thus it is possible to use DUNE even in proprietary software. The underlying idea of DUNE is to create slim interfaces allowing an efficient use of legacy and/or new libraries. Modern C++ programming techniques enable very different implementations of the same concept (i.e. grids, solvers, ...) using a common interface at a very low overhead. Thus DUNE ensures efficiency in scientific computations and supports high-performance computing applications. DUNE is based on the following main principles:

• Separation of data structures and algorithms by abstract interfaces.- This provides more functionality with less code and also ensures maintainability and extendability of the framework.
• Efficient implementation of these interfaces using generic programming techniques.
• Static polymorphism allows the compiler to do more optimizations, in particular function inlining, which in turn allows the interface to have very small functions (implemented by one or few machine instructions) without a severe performance penalty. In essence the algorithms are parametrized with a particular data structure and the interface is removed at compile time. Thus the resulting code is as efficient as if it would have been written for the special case.
• Reuse of existing finite element packages with a large body of functionality.- In particular the finite element codes UG, ALBERTA, and ALUGrid have been adapted to the DUNE framework. Thus, parallel and adaptive meshes with multiple element types and refinement rules are available. All these packages can be linked together in one executable.
• The framework consists of a number of modules which are downloadable as separate packages. The current core modules are:
• dune-common- contains the basic classes used by all DUNE-modules. It provides some infrastructural classes for debugging and exception handling as well as a library to handle dense matrices and vectors.
• dune-grid- is the most mature module. It defines nonconforming, hierarchically nested, multi-element-type, parallel grids in arbitrary space dimensions. Graphical output with several packages is available, e.g. file output to IBM data explorer and VTK (parallel XML format for unstructured grids). The graphics package Grape has been integrated in interactive mode.
• dune-istl (Iterative Solver Template Library)- provides generic sparse matrix/vector classes and a variety of solvers based on these classes. A special feature is the use of templates to exploit the recursive block structure of finite element matrices at compile time. Available solvers include Krylov methods, (block-) incomplete decompositions and aggregation-based algebraic multigrid.

DUNE-Istl DUNE, the Distributed and Unified Numerics Environment is a modular toolbox for solving partial differential equations (PDEs) with grid-based methods. It supports the easy implementation of methods like Finite Elements (FE), Finite Volumes (FV), and also Finite Differences (FD). DUNE is free software licensed under the GPL (version 2) with a so called "runtime exception" (see license). This licence is similar to the one under which the libstdc++ libraries are distributed. Thus it is possible to use DUNE even in proprietary software. The underlying idea of DUNE is to create slim interfaces allowing an efficient use of legacy and/or new libraries. Modern C++ programming techniques enable very different implementations of the same concept (i.e. grids, solvers, ...) using a common interface at a very low overhead. Thus DUNE ensures efficiency in scientific computations and supports high-performance computing applications. DUNE is based on the following main principles:

• Separation of data structures and algorithms by abstract interfaces.- This provides more functionality with less code and also ensures maintainability and extendability of the framework.
• Efficient implementation of these interfaces using generic programming techniques.
• Static polymorphism allows the compiler to do more optimizations, in particular function inlining, which in turn allows the interface to have very small functions (implemented by one or few machine instructions) without a severe performance penalty. In essence the algorithms are parametrized with a particular data structure and the interface is removed at compile time. Thus the resulting code is as efficient as if it would have been written for the special case.
• Reuse of existing finite element packages with a large body of functionality.- In particular the finite element codes UG, ALBERTA, and ALUGrid have been adapted to the DUNE framework. Thus, parallel and adaptive meshes with multiple element types and refinement rules are available. All these packages can be linked together in one executable.
• The framework consists of a number of modules which are downloadable as separate packages. The current core modules are:
• dune-common- contains the basic classes used by all DUNE-modules. It provides some infrastructural classes for debugging and exception handling as well as a library to handle dense matrices and vectors.
• dune-grid- is the most mature module. It defines nonconforming, hierarchically nested, multi-element-type, parallel grids in arbitrary space dimensions. Graphical output with several packages is available, e.g. file output to IBM data explorer and VTK (parallel XML format for unstructured grids). The graphics package Grape has been integrated in interactive mode.
• dune-istl (Iterative Solver Template Library)- provides generic sparse matrix/vector classes and a variety of solvers based on these classes. A special feature is the use of templates to exploit the recursive block structure of finite element matrices at compile time. Available solvers include Krylov methods, (block-) incomplete decompositions and aggregation-based algebraic multigrid.

Dap Dap is a small statistics and graphics package, based on C, that provides core methods of data management, analysis, and graphics commonly used in statistical consulting practice. Anyone familiar with basic C syntax can learn Dap quickly and easily from the manual and the examples in it. Advanced features of C are not necessary, although they are available. As of Version 3.0, Dap can read SBS programs, thereby freeing the user from having to learn any C at all to run straightforward analyses. The manual contains a brief introduction to the C syntax needed for C-style programming for Dap. Because Dap processes files one line at a time, rather than reading entire files into memory, it can be, and has been, used on data sets that have very many lines and/or very many variables.

DataCaptureTool DataCapture was born out of frustration, and after much procrastination. Every time I had to get numerical values of a graph from a journal or a conference paper, I had to painstakingly approximate data points from the graph as best I could. Every time the points would come out inaccurate and a rather poor reproduction of the actual data. I wanted to write a program that would automate this task, and do a much better job at that. But then, that was three years ago. Finally its done. Its not the best thing that I have created, but certainly, one of the most useful. Its written in TCl/Tk and is a very small and uncomplicated aplication. Something that you can easily incorporate into your own applications easily.

Easyval 'Easyval' is a basic implementation of interval arithmetic that uses hardware doubles as interval bounds. The first goal of this library is to respect the interval arithmetic containment criterium.